Board tells shareholders £230m valuation "wholly inadequate"
The Dundee life sciences firm, which makes testing kits for diabetes and rheumatoid arthritis, said the 460 pence per share offer is "wholly inadequate".
Just one per cent of Axis' shareholders have backed the offer from Alere which values the company at £230 million.
The deal deadline has been extended again until October 10.
Massachusetts-based Alere said "persistent negative economic news" since its initial July offer has seen Axis-Shield's share price drop by 20 per cent.
It warns the price could fall significantly below its current share price, "particularly as no other potential bidder has announced its interest publicly".
The American firm has also dropped a bid condition requiring 90 per cent shareholder approval to 50 per cent, which would give it a controlling stake in Axis-Shield.
However, the board of Axis-Shield says the bid significantly undervalues the company and accuses Alere of trying to buy the company "on the cheap".
In a market statement, Axis-Shield, said: "The Board has been more than willing to engage with Alere if Alere were to put a proposal to the Board that fairly reflected the fundamental value of Axis-Shield. To date, no such proposal has been received from Alere.
"The Company has made excellent progress in the first half of the year and is on track to deliver for the second half of the year.
"The Company believes that Alere is making a highly opportunistic offer in order to try and acquire Axis-Shield on the cheap."